Galois Theory and Advanced Linear Algebra
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Beschreibung
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
Discusses the fundamental topics in Galois theory and advanced linear algebra Serves as an easy-to-understand textbook for undergraduate students of linear algebra Helps students understand other courses, such as Riemannian geometry
Autor*in
Rajnikant Sinha
Themen in »Galois Theory and Advanced Linear Algebra«
Galois Theory Canonical Forms Euclidean Rings Polynomial Rings The Eisenstein Criterion Splitting Fields Linear Algebra Eigenvalues Cayley-Hamilton Theorem Sylvester’s Law